A turntable of moment of inertia I0 rotates freely on a hollow vertical axis. A cart of mass m runs without friction on a straight radial track on the turntable. A cord attached to the cart passes over a small pulley and then downward through the hollow axis. Initially the entire system is rotating at angular speed ω0, and the cart is at a fixed radius R from the axis. The cart is then pulled inward by applying an excess force to the cord, and eventually arrives at radius r, where it is allowed to remain.
a)
What is the new angular velocity of the system?
b)
Show in detail that the difference in the energy of the system
between the two conditions is equal to the work done by the centripetal
force.
c) If the cord is released, with what radial speed, dr/dt, will the cart pass the radius R?
Answer :